The value of the integral ∫ 0 1 2 1 + 3 x + 1 2 1 - x 6 1 4   d x is

Question

The value of the integral &#8747; 0 1 2 1 + 3 x + 1 2 1 - x 6 1 4 &#160; d x is

Aicharya · Accepted Answer

&#8747; 0 1 2 1 + 3 d x 1 + x 2 1 - x 6 1 4 &#8747; 0 1 2 1 + 3 d x 1 + x 2 1 - x 6 1 + x 6 1 4 Put 1 - x 1 + x = t &#8658; - 2 d x 1 + x 2 = d t I = &#8747; 1 1 3 1 + 3 d t - 2 t 6 4 = - 1 + 3 2 &#215; - 2 t 1 1 3 = 1 + 3 &#160; 3 - 1 = 2

The value of the integral &#8747; 0 1 2 1 + 3 x + 1 2 1 - x 6 1 4 &#160; d x is

Solution

The value of the integral ∫ 0 1 2 1 + 3 x + 1 2 1 - x 6 1 4 d x is